Solve 3(2x^2)-2x=2(3x-6)

Question

Solve the equation(The real numbers system)

x \in / R

Alternative Form

No real solution

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Solve using the quadratic formula in the complex numbers system

Solve by completing the square in the complex numbers system

Solve using the PQ formula in the complex numbers system

x_{1} = \frac{2}{3} - \frac{14}{3} i, x_{2} = \frac{2}{3} + \frac{14}{3} i

Alternative Form

x_{1} \approx 0. \dot{6} - 1.247219 i, x_{2} \approx 0. \dot{6} + 1.247219 i

Evaluate

3 \times 2 x^{2} - 2 x = 2 (3 x - 6)

Multiply the numbers

6 x^{2} - 2 x = 2 (3 x - 6)

Expand the expression

More Steps

6 x^{2} - 2 x = 6 x - 12

Move the expression to the left side

6 x^{2} - 8 x + 12 = 0

Substitute a= 6,b= - 8 and c= 12 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{8 \pm ( - 8 ) ^{2} - 4 \times 6 \times 12}{2 \times 6}

Simplify the expression

x = \frac{8 \pm ( - 8 ) ^{2} - 4 \times 6 \times 12}{12}

Simplify the expression

More Steps

x = \frac{8 \pm - 224}{12}

Simplify the radical expression

More Steps

x = \frac{8 \pm 4 14 \times i}{12}

Separate the equation into 2 possible cases

x = \frac{8 + 4 14 \times i}{12} x = \frac{8 - 4 14 \times i}{12}

Simplify the expression

More Steps

x = \frac{2}{3} + \frac{14}{3} i x = \frac{8 - 4 14 \times i}{12}

Simplify the expression

More Steps

x = \frac{2}{3} + \frac{14}{3} i x = \frac{2}{3} - \frac{14}{3} i

Solution

x_{1} = \frac{2}{3} - \frac{14}{3} i, x_{2} = \frac{2}{3} + \frac{14}{3} i

Alternative Form

x_{1} \approx 0. \dot{6} - 1.247219 i, x_{2} \approx 0. \dot{6} + 1.247219 i

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